What is wrong with the implementation of Prim's algorithm?

Question

C++ / C#

I am trying to solve problem 1160. Network . It seems to me that to solve it you need to find a spanning tree, so I decided to use Prim's algorithm. Unfortunately, there is an error on test 5. What could be wrong? All my tests pass.

#include <iostream>;
#include <vector>;

void primAlgorithm(std::vector<std::vector<int>>& matrix, std::vector<int>& parent, std::vector<int>& minValue, std::vector<bool>& isPartOfOutputTree)
{
  minValue[0] = 0;
  parent[0] = -1;
  for (int i = 0; i < matrix.size(); i++) 
  {
    int minIndex = -1;
    for (int j = 0; j < matrix.size(); j++)
      if ((!isPartOfOutputTree[j]) && ((minIndex == -1) || (minValue[minIndex] > minValue[j])))
        minIndex = j;

    isPartOfOutputTree[minIndex] = true;

    for (int j = 0; j < matrix.size(); j++)
      if ((matrix[minIndex][j] < minValue[j]))
      {
        parent[j] = minIndex;
        minValue[j] = matrix[minIndex][j];
      }
  }
}

int main() 
{
  int n = 0, m = 0;
  std::cin >> n >> m;
  std::vector<std::vector<int>> matrix(n, std::vector<int>(n, 1000001));
  std::vector<int> parent(n), minValue(n, 1000001);
  std::vector<bool> isPartOfOutputTree(n);

  for (int i = 0; i < m; i++) 
  {
    int first = 0, second = 0, length = 0;
    std::cin >> first >> second >> length;
    matrix[first - 1][second - 1] = length;
    matrix[second - 1][first - 1] = length;
  }

  primAlgorithm(matrix, parent, minValue, isPartOfOutputTree);

  int maxLength = matrix[1][parent[1]];
  for (int i = 1; i < n; i++)
    if (matrix[i][parent[i]] > maxLength) maxLength = matrix[i][parent[i]];

  std::cout << maxLength << '\n' << n - 1 << '\n';
  for (int i = 1; i < n; i++)
    std::cout << parent[i] + 1 << ' ' << i + 1 << '\n';
}

Answer 1

if ((matrix[i][j] < minValue[j]) && (isPartOfOutputTree[j] == false))

Here is the error. After all, i is the iteration number, and not at all the vertex just included in the tree, with respect to which relaxation must be done.